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Unit Rates & Conversions How to set up & solve conversions using the unit rate Let’s Review Unit Rate Unit Rate is a comparison of two amounts with different units and one of the units equals 1. Example: 12 inches = 1 foot This is a unit rate because there are two different units, and one of the units (foot) equals 1. More examples of a Unit Rate Example: 4 quarters = 1 dollar This is a unit rate because there are two different units, and one of the units (dollar) equals 1. Example: 1 McDonald’s sausage biscuit = 430 calories This is a unit rate because there are two different units, and one of the units (McDonald’s sausage biscuit) equals 1. Other Examples of Unit Rates Speedometers tell how fast a vehicle is moving… in miles per hour. We see unit rates around us all of the time… we just do not realize they are there! Road signs tell us what the speed limit is that we can drive. In this case, it’s 45 mph (miles per hour) What we usually do not realize, is that Miles Per Hour is actually saying Miles Per 1 Hour! Hey! That’s a unit rate! Here we are… at the gas station! These prices are telling us the cost per gallon, or the cost per 1 gallon! That’s a Unit Rate! So… Key Word… per When I see the word per …. I know… That’s a Unit Rate! How do Unit Rates help in the Real World? You use unit rates so much, you don’t even realize it! If one bag of Takis cost $1, how much would 12 bags of Takis cost? You guessed it… $12! You used the amount it costs for ONE bag of Takis, and multiplied it to find the amount for 12 bags… That’s called using the Unit Rate! But when else…. Would I use unit rate? Mr. Wilson spent $252 to stay 3 nights at Days Inn. At that rate, how much will he spend to stay 7 nights? You can try to set it up like we usually do… $ 252 Nights 3 x x? 7 But can you figure out the Constant of Proportionality here? Mr. Wilson spent $252 to stay 3 nights at Days Inn. At that rate, how much will he spend to stay 7 nights? It will cost Mr. Wilson $588 for 7 nights. Let’s try finding the Unit Rate, first! Remember, unit rate makes one of the units equal 1. $ ℎ ÷3 = 252 3 = ÷3 1 We divide the 3 nights to one night Now that we know the unit rate is 1 night = $84, we can use it to figure out 7 nights! $ ℎ = 84 1 = x7 7 Wait a Minute! What did we do to solve that last problem? (raise your hand and let’s review the steps) Conversions In order to solve some real world problems, we have to use our logical thinking! We will not have exactly what we need to solve a problem. BUT We can use other information that we already know to help us solve the problem. We can then change or convert what we know to the unit we need to solve the problem. Information We Should Know Example: How many feet are in 12 yards? To answer this question, I need to know how many feet are in 1 yard. 1 yard = 3 feet The above unit rate is not in the problem, but I have to use it to solve! Feet Yards x3 3 X 1 12 x3 12 yards = 36 feet Example: 32 pints = __ gallons To solve this question, I need to know how many pints are in 1 gallon. UH OH! When I check my table, it does not tell me how many pints are in 1 gallon! That means, I have to use another unit rate to find out the unit rate I need! Example: 32 pints = __ gallons The chart says: 1 quart= 2 pints & 1 gallon = 4 quarts I have 1 quart, but I need 4! Quart 1 x 4 =4 Pints 2 x 4 =8 So… 4 quarts = 8 pints If 4 quarts = 8 pints And 4 quarts = 1 gallon Then 8 pints = 1 gallon! Example: 32 pints = __ gallons The chart says: 1 quart= 2 pints & 1 gallon = 4 quarts I have 1 quart, but I need 4! Quart 1 x 4 =4 Pints 2 x 4 =8 Pints 8 x4 32 Gallons 1 x4 x So… 4 quarts = 8 pints If 4 quarts = 8 pints And 4 quarts = 1 gallon Then 8 pints = 1 gallon! 32 pints = 4 gallons Practice with Your Elbow Buddy